What's the benefit of initiating followers into the Blades?
Once you've discovered Sky Haven Temple, Delphine Jend tells you that if you'd like to expand the ranks of the Blades, you can bring followers to her, and she'll administer the oath and induct them into the Blades.
What's the benefit of this? Is it just the 'upgrade' to their default equipment? Or do their 'tagged' skills change at all?
The only other benefit that I can see is that for those followers with out of the way or inconvenient 'homes', you can relocate them to Sky Haven for much easier recruitment. This is particularly handy for the Khajit caravaeer I suppose.
Solution 1:
When you get a quest to kill a dragon from Esbern in Sky Haven Temple, your recuited Blades(up to three it seems) will help you kill that dragon if you want. It's overkill really, but there you go.
Solution 2:
The Blades were all hunted down to the point of extinction, so much so that the Dovahkiin only knows two of their number (Delphine and Esbern). By recruiting more members into The Blades, you are bolstering their ranks and helping them regain some semblance of their former selves.
This is not unlike restoring some other low reputation groups to their former glory (Thieves Guild, Dark Brotherhood).
Now this is a deeply personal conjecture on my part, but it gives a sense of accomplishment. Having helped the other groups to regain their former glory, recruiting new members into The Blades feels the same way. Also it remains to be seen if this might have any future impact like say via DLC or the next TES sequel.